JEE Main 5 April 2024 Shift 1 Question Paper

Question 1

Let $d$ be the distance of the point of intersection of the lines $\dfrac{x+6}{3}=\dfrac{y}{2}=\dfrac{z+1}{1}$ and $\dfrac{x-7}{4}=\dfrac{y-9}{3}=\dfrac{z-4}{2}$ from the point $(7, 8, 9)$. Then $d^2 + 6$ is equal to:

Accepted Answer

(C) $75$

Answer

(A) $72$

Answer

(B) $69$

Answer

(D) $78$

Question 2

Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let $a$ and $b$ be the sides of the rectangle PQRS when its area is maximum. Then $(a + b)^2$ is equal to:

Accepted Answer

(A) $72$

Answer

(B) $60$

Answer

(C) $80$

Answer

(D) $64$

Question 3

Let two straight lines drawn from the origin O intersect the line $3x + 4y = 12$ at the points P and Q such that $\Delta OPQ$ is an isosceles triangle and $\angle POQ = 90^\circ$. If $l = OP^2 + PQ^2 + QO^2$, then the greatest integer less than or equal to $l$ is:

Accepted Answer

(C) $46$

Answer

(A) $44$

Answer

(B) $48$

Answer

(D) $42$

Question 4

If $y = y(x)$ is the solution of the differential equation $\dfrac{dy}{dx} + 2y = \sin(2x)$, $y(0) = \dfrac{3}{4}$, then $y\left(\dfrac{\pi}{8}\right)$ is equal to:

Accepted Answer

(B) $e^{-\pi/4}$

Answer

(A) $e^{-\pi/8}$

Answer

(C) $e^{\pi/4}$

Answer

(D) $e^{\pi/8}$

Question 5

For the function $f(x) = \sin x + 3x - \dfrac{2}{\pi}(x^2 + x)$, where $x \in \left[0, \dfrac{\pi}{2}\right]$, consider the following two statements: (I) $f$ is increasing in $\left(0, \dfrac{\pi}{2}\right)$. (II) $f'$ is decreasing in $\left(0, \dfrac{\pi}{2}\right)$. Between the above two statements,

Accepted Answer

(D) both (I) and (II) are true.

Answer

(A) only (I) is true.

Answer

(B) only (II) is true.

Answer

(C) neither (I) nor (II) is true.

Question 6

If the system of equations $11x + y + \lambda z = -5$, $2x + 3y + 5z = 3$, $8x - 19y - 39z = \mu$ has infinitely many solutions, then $\lambda^4 - \mu$ is equal to:

Accepted Answer

(C) $47$

Answer

(A) $49$

Answer

(B) $45$

Answer

(D) $51$

Question 7

Let $A = \{1, 3, 7, 9, 11\}$ and $B = \{2, 4, 5, 7, 8, 10, 12\}$. Then the total number of one-one maps $f : A 	o B$, such that $f(1) + f(3) = 14$, is:

Accepted Answer

(D) $240$

Answer

(A) $180$

Answer

(B) $120$

Answer

(C) $480$

Question 8

If the function $f(x) = \dfrac{\sin 3x + \alpha \sin x - \beta \cos 3x}{x^3}$, $x \in \mathbb{R}$, is continuous at $x = 0$, then $f(0)$ is equal to:

Accepted Answer

(D) $-4$

Answer

(A) $2$

Answer

(B) $-2$

Answer

(C) $4$

Question 9

The integral $\displaystyle\int_{0}^{\pi/4} \dfrac{136\sin x}{3\sin x + 5\cos x}\,dx$ is equal to:

Accepted Answer

(A) $3\pi - 50\log_e 2 + 20\log_e 5$

Answer

(B) $3\pi - 25\log_e 2 + 10\log_e 5$

Answer

(C) $3\pi - 10\log_e\left(2\sqrt{2}\right) + 10\log_e 5$

Answer

(D) $3\pi - 30\log_e 2 + 20\log_e 5$

Question 10

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$. The probability of this equation having repeated roots is:

Accepted Answer

(C) $\dfrac{1}{64}$

Answer

(A) $\dfrac{3}{256}$

Answer

(B) $\dfrac{1}{128}$

Answer

(D) $\dfrac{3}{128}$

Question 11

Let A and B be two square matrices of order 3 such that $|A| = 3$ and $|B| = 2$. Then $\left|A^T A(	ext{adj}(2A))^{-1} (	ext{adj}(4B))(	ext{adj}(AB))^{-1} A A^Tight|$ is equal to:

Accepted Answer

(A) $64$

Answer

(B) $81$

Answer

(C) $32$

Answer

(D) $108$

Question 12

Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point $(3, 2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point $(5, 5)$ is:

Accepted Answer

(D) $4$

Answer

(A) $2\sqrt{2}$

Answer

(B) $5$

Answer

(C) $4\sqrt{2}$

Question 13

Let the line $2x + 3y - k = 0$, $k > 0$, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is $x^2 + y^2 - 3x - 2y = 0$ and the length of the latus rectum of the ellipse $x^2 + 9y^2 = k^2$ is $\dfrac{m}{n}$, where m and n are coprime, then $2m + n$ is equal to:

Accepted Answer

(B) $11$

Answer

(A) $10$

Answer

(C) $13$

Answer

(D) $12$

Question 14

Consider the following two statements:
Statement I: For any two non-zero complex numbers $z_1, z_2$, $(|z_1| + |z_2|)\left|\dfrac{z_1}{|z_1|} + \dfrac{z_2}{|z_2|}\right| \le 2(|z_1| + |z_2|)$ and
Statement II: If $x, y, z$ are three distinct complex numbers and $a, b, c$ are three positive real numbers such that $\dfrac{a}{|y-z|} = \dfrac{b}{|z-x|} = \dfrac{c}{|x-y|}$, then $\dfrac{a^2}{y-z} + \dfrac{b^2}{z-x} + \dfrac{c^2}{x-y} = 1$. Between the above two statements,

Accepted Answer

(C) Statement I is correct but Statement II is incorrect.

Answer

(A) both Statement I and Statement II are incorrect.

Answer

(B) Statement I is incorrect but Statement II is correct.

Answer

(D) both Statement I and Statement II are correct.

Question 15

Suppose $	heta \in \left[0, \dfrac{\pi}{4}ight]$ is a solution of $4\cos	heta - 3\sin	heta = 1$. Then $\cos	heta$ is equal to:

Accepted Answer

(A) $\dfrac{4}{\left(3\sqrt{6} - 2\right)}$

Answer

(B) $\dfrac{6 - \sqrt{6}}{\left(3\sqrt{6} - 2\right)}$

Answer

(C) $\dfrac{6 + \sqrt{6}}{\left(3\sqrt{6} + 2\right)}$

Answer

(D) $\dfrac{4}{\left(3\sqrt{6} + 2\right)}$

Question 16

If $\dfrac{1}{\sqrt{1}+\sqrt{2}} + \dfrac{1}{\sqrt{2}+\sqrt{3}} + \ldots + \dfrac{1}{\sqrt{99}+\sqrt{100}} = m$ and $\dfrac{1}{1\cdot 2} + \dfrac{1}{2\cdot 3} + \ldots + \dfrac{1}{99\cdot 100} = n$, then the point $(m, n)$ lies on the line:

Accepted Answer

(D) $11x - 100y = 0$

Answer

(A) $11(x - 1) - 100(y - 2) = 0$

Answer

(B) $11(x - 2) - 100(y - 1) = 0$

Answer

(C) $11(x - 1) - 100y = 0$

Question 17

Let $f(x) = x^5 + 2x^3 + 3x + 1$, $x \in \mathbb{R}$, and $g(x)$ be a function such that $g(f(x)) = x$ for all $x \in \mathbb{R}$. Then $\dfrac{g(7)}{g'(7)}$ is equal to:

Accepted Answer

(D) $14$

Answer

(A) $7$

Answer

(B) $42$

Answer

(C) $1$

Question 18

If $A(1, -1, 2)$, $B(5, 7, -6)$, $C(3, 4, -10)$ and $D(-1, -4, -2)$ are the vertices of a quadrilateral ABCD, then its area is:

Accepted Answer

(A) $12\sqrt{29}$

Answer

(B) $24\sqrt{29}$

Answer

(C) $24\sqrt{7}$

Answer

(D) $48\sqrt{7}$

Question 19

The value of $\displaystyle\int_{-\pi}^{\pi} \dfrac{2y(1+\sin y)}{1+\cos^2 y}\,dy$ is:

Accepted Answer

(A) $\pi^2$

Answer

(B) $\dfrac{\pi^2}{2}$

Answer

(C) $\dfrac{\pi}{2}$

Answer

(D) $2\pi^2$

Question 20

If the line $\dfrac{2-x}{3} = \dfrac{3y-2}{4\lambda+1} = 4 - z$ makes a right angle with the line $\dfrac{x+3}{3\mu} = \dfrac{1-2y}{6} = \dfrac{5-z}{7}$, then $4\lambda + 9\mu$ is equal to:

Accepted Answer

(D) $6$

Answer

(A) $13$

Answer

(B) $4$

Answer

(C) $5$

Question 21

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is $\sigma^2$, then $96\sigma^2$ is equal to ___.

Accepted Answer

56

Question 22

If the constant term in the expansion of $\left(1 + 2x - 3x^3\right)\left(\dfrac{3}{2}x^2 - \dfrac{1}{3x}\right)^9$ is $p$, then $108p$ is equal to ___.

Accepted Answer

54

Question 23

The area of the region enclosed by the parabolas $y = x^2 - 5x$ and $y = 7x - x^2$ is ___.

Accepted Answer

72

Question 24

The number of ways of getting a sum 16 on throwing a dice four times is ___.

Accepted Answer

125

Question 25

If $S = \{a \in \mathbb{R} : |2a - 1| = 3[a] + 2\{a\}\}$, where $[t]$ denotes the greatest integer less than or equal to $t$ and $\{t\}$ represents the fractional part of $t$, then $72\displaystyle\sum_{a \in S} a$ is equal to ___.

Accepted Answer

18

Question 26

Let $f$ be a differentiable function in the interval $(0, \infty)$ such that $f(1) = 1$ and $\displaystyle\lim_{t 	o x} \dfrac{t^2 f(x) - x^2 f(t)}{t - x} = 1$ for each $x > 0$. Then $2f(2) + 3f(3)$ is equal to ___.

Accepted Answer

24

Question 27

Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms. Let $A_k = a_1^2 - a_2^2 + a_3^2 - a_4^2 + \ldots + a_{2k-1}^2 - a_{2k}^2$. If $A_3 = -153$, $A_5 = -435$ and $a_1^2 + a_2^2 + a_3^2 = 66$, then $a_{17} - A_7$ is equal to ___.

Accepted Answer

910

Question 28

Let $\vec{a} = \hat{i} - 3\hat{j} + 7\hat{k}$, $\vec{b} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{c}$ be a vector such that $(\vec{a} + 2\vec{b}) 	imes \vec{c} = 3(\vec{c} 	imes \vec{a})$. If $\vec{a} \cdot \vec{c} = 130$, then $\vec{b} \cdot \vec{c}$ is equal to ___.

Accepted Answer

30

Question 29

The number of distinct real roots of the equation $|x|\,|x + 2| - 5|x + 1| - 1 = 0$ is ___.

Accepted Answer

3

Question 30

Suppose $AB$ is a focal chord of the parabola $y^2 = 12x$ of length $l$ and slope $m < \sqrt{3}$. If the distance of the chord $AB$ from the origin is $d$, then $ld^2$ is equal to ___.

Accepted Answer

108

Question 31

Light emerges out of a convex lens when a source of light is kept at its focus. The shape of wavefront of the light is:

Accepted Answer

(D) Plane

Answer

(A) Both spherical and cylindrical

Answer

(B) Cylindrical

Answer

(C) Spherical

Question 32

A combination of logic gates is connected in a complete suitable circuit (shown in the figure). For which of the following input combinations will the bulb glow (ON)?

Accepted Answer

(B) A = 1, B = 0, C = 0, D = 0

Answer

(A) A = 0, B = 1, C = 1, D = 1

Answer

(C) A = 0, B = 0, C = 0, D = 1

Answer

(D) A = 1, B = 1, C = 1, D = 0

Question 33

If G is the gravitational constant and $u$ is the energy density then which of the following quantity has the same dimensions as $\sqrt{uG}$:

Accepted Answer

(B) Force per unit mass

Answer

(A) Pressure gradient per unit mass

Answer

(C) Gravitational potential

Answer

(D) Energy per unit mass

Question 34

Given below are two statements:
Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $90^{\circ}$.
Statement-II: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

(A) Statement-I is false and Statement-II is true.

Answer

(B) Both Statement-I and Statement-II are true.

Answer

(C) Both Statement-I and Statement-II are false.

Answer

(D) Statement-I is true and Statement-II is false.

Question 35

Given below are two statements:
Statement-I: The figure shows the variation of stopping potential with frequency ($
u$) for two photosensitive materials $M_1$ and $M_2$. The slope gives the value of $\dfrac{h}{e}$, where $h$ is Planck’s constant and $e$ is the charge of the electron.
Statement-II: $M_2$ will emit photoelectrons of greater kinetic energy for incident radiation having the same frequency.
In the light of the above statements, choose the most appropriate answer from the options given below.

Accepted Answer

(A) Statement-I is correct and Statement-II is incorrect.

Answer

(B) Statement-I is incorrect but Statement-II is correct.

Answer

(C) Both Statement-I and Statement-II are incorrect.

Answer

(D) Both Statement-I and Statement-II are correct.

Question 36

The angle between vector $\vec{Q}$ and the resultant of $(2\vec{Q}+2\vec{P})$ and $(2\vec{Q}-2\vec{P})$ is:

Accepted Answer

(A) $0^{\circ}$

Answer

(B) $	an^{-1}\left(\dfrac{2\vec{Q}-2\vec{P}}{2\vec{Q}+2\vec{P}}ight)$

Answer

(C) $	an^{-1}\left(\dfrac{P}{Q}ight)$

Answer

(D) $	an^{-1}\left(\dfrac{2Q}{P}ight)$

Question 37

In a hydrogen-like system the ratio of the Coulomb force and the gravitational force between an electron and a proton is of the order of:

Accepted Answer

(A) $10^{39}$

Answer

(B) $10^{19}$

Answer

(C) $10^{29}$

Answer

(D) $10^{36}$

Question 38

In a coaxial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero:

Accepted Answer

(C) outside the cable

Answer

(A) inside the outer conductor

Answer

(B) in between the two conductors

Answer

(D) inside the inner conductor

Question 39

An electron rotates in a circle around a nucleus having positive charge $Ze$. The correct relation between the total energy (E) of the electron and its potential energy (U) is:

Accepted Answer

(D) $2E = U$

Answer

(A) $E = 2U$

Answer

(B) $2E = 3U$

Answer

(C) $E = U$

Question 40

If the collision frequency of hydrogen molecules in a closed chamber at $27^{\circ}	ext{C}$ is $Z$, then the collision frequency of the same system at $127^{\circ}	ext{C}$ is:

Accepted Answer

(C) $\dfrac{2}{\sqrt{3}}Z$

Answer

(A) $\dfrac{\sqrt{3}}{2}Z$

Answer

(B) $\dfrac{4}{3}Z$

Answer

(D) $\dfrac{3}{4}Z$

Question 41

The ratio of the radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for the moment of inertia about their diameter axis AB as shown in the figure, is $\sqrt{\dfrac{8}{x}}$. The value of $x$ is:

Accepted Answer

(C) 67

Answer

(A) 34

Answer

(B) 17

Answer

(D) 51

Question 42

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in the figure (radius of A is $a$, radius of B is $b$, with $b \gg a$). The mutual inductance between them is:

Accepted Answer

(A) $\dfrac{\mu_0\pi a^2}{2b}$

Answer

(B) $\dfrac{\mu_0}{2\pi}\dfrac{b^2}{a}$

Answer

(C) $\dfrac{\mu_0\pi b^2}{2a}$

Answer

(D) $\dfrac{\mu_0}{2\pi}\dfrac{a^2}{b}$

Question 43

Match List-I (energies of a planet of mass $m$ in a circular orbit of radius $a$ around the Sun of mass $M$; $r$ = radius of the planet) with List-II (their expressions). Choose the correct answer from the options given below.

Accepted Answer

(A) (A)–II, (B)–I, (C)–IV, (D)–III

Answer

(B) (A)–III, (B)–IV, (C)–I, (D)–II

Answer

(C) (A)–I, (B)–IV, (C)–II, (D)–III

Answer

(D) (A)–I, (B)–II, (C)–III, (D)–IV

Question 44

A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on top of the block, the floor yields and the block and cylinder together go down with an acceleration of $0.1\ 	ext{ms}^{-2}$. The action force of the system on the floor is equal to:

Accepted Answer

(C) 291 N

Answer

(A) 297 N

Answer

(B) 294 N

Answer

(D) 196 N

Question 45

A simple pendulum doing small oscillations at a place at height R above the earth’s surface has time period $T_1 = 4$ s. $T_2$ would be its time period if it is brought to a point at height 2R from the earth’s surface. Choose the correct relation [R = radius of Earth]:

Accepted Answer

(C) $3T_1 = 2T_2$

Answer

(A) $T_1 = T_2$

Answer

(B) $2T_1 = 3T_2$

Answer

(D) $2T_1 = T_2$

Question 46

A body of mass 50 kg is lifted to a height of 20 m from the ground in two different ways as shown in the figures. The ratio of the work done against gravity in the two respective cases will be:

Accepted Answer

(A) 1 : 1

Answer

(B) 2 : 1

Answer

(C) $\sqrt{3}:2$

Answer

(D) 1 : 2

Question 47

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings to the correct significant figures is:

Accepted Answer

(C) 4.6 s

Answer

(A) 4.623 s

Answer

(B) 4.62 s

Answer

(D) 5 s

Question 48

The heat absorbed by a system in going through the given cyclic process is:

Accepted Answer

(A) 61.6 J

Answer

(B) 431.2 J

Answer

(C) 616 J

Answer

(D) 19.6 J

Question 49

In the given figure $R_1 = 10\ \Omega$, $R_2 = 8\ \Omega$, $R_3 = 4\ \Omega$ and $R_4 = 8\ \Omega$. The battery is ideal with emf 12 V. The equivalent resistance of the circuit and the current supplied by the battery are respectively:

Accepted Answer

(D) $12\ \Omega$ and $1\ 	ext{A}$

Answer

(A) $12\ \Omega$ and $11.4\ 	ext{A}$

Answer

(B) $10.5\ \Omega$ and $1.14\ 	ext{A}$

Answer

(C) $10.5\ \Omega$ and $1\ 	ext{A}$

Question 50

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across a capacitor of $12\ \mu	ext{F}$. The maximum displacement current between the plates of the capacitor is nearly:

Accepted Answer

(D) 12 A

Answer

(A) 13 A

Answer

(B) 8 A

Answer

(C) 10 A

Question 51

In Young’s double slit experiment, carried out with light of wavelength $5000\ 	ext{Å}$, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x = 0$ cm. The value of $x$ for the third maximum is ___ mm.

Accepted Answer

10

Question 52

A 2 A current-carrying straight metal wire of resistance $1\ \Omega$, resistivity $2	imes10^{-6}\ \Omega\,	ext{m}$, area of cross-section $10\ 	ext{mm}^2$ and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of B is ___ $	imes10^{-1}$ T (given $g = 10\ 	ext{m/s}^2$).

Accepted Answer

5

Question 53

The electric field between the two parallel plates of a capacitor of $1.5\ \mu	ext{F}$ capacitance drops to one third of its initial value in $6.6\ \mu	ext{s}$ when the plates are connected by a thin wire. The resistance of this wire is ___ $\Omega$. (Given $\log 3 = 1.1$.)

Accepted Answer

4

Question 54

Three blocks $M_1$, $M_2$, $M_3$ of masses 4 kg, 6 kg and 10 kg respectively hang from a smooth pulley using ropes 1, 2 and 3 in succession (rope 1 at the top carries all three, rope 2 carries $M_2$ and $M_3$, rope 3 carries $M_3$). The tension $T_1$ in rope 1 when they move upward with acceleration $2\ 	ext{ms}^{-2}$ is ___ N (with $g = 10\ 	ext{m/s}^2$).

Accepted Answer

240

Question 55

The density and breaking stress of a wire are $6	imes10^4\ 	ext{kg/m}^3$ and $1.2	imes10^8\ 	ext{N/m}^2$ respectively. The wire is suspended from a rigid support on a planet where the acceleration due to gravity is $\dfrac{1}{3}$ of the value on the surface of earth. The maximum length of the wire without breaking is ___ m (take $g = 10\ 	ext{m/s}^2$).

Accepted Answer

600

Question 56

A body moves on a frictionless plane starting from rest. If $S_n$ is the distance moved between $t = n-1$ and $t = n$ and $S_{n-1}$ is the distance moved between $t = n-2$ and $t = n-1$, then the ratio $\dfrac{S_{n-1}}{S_n}$ is $\left(1-\dfrac{2}{x}\right)$ for $n = 10$. The value of $x$ is ___.

Accepted Answer

19

Question 57

If three helium nuclei combine to form a carbon nucleus, then the energy released in this reaction is ___ $	imes10^{-2}$ MeV. (Given $1\ 	ext{u} = 931\ 	ext{MeV}/c^2$; atomic mass of helium = 4.002603 u; mass of carbon-12 = 12 u.)

Accepted Answer

727

Question 58

An ac source $V = 50\sqrt{2}\sin(100t)$ V is connected in a series LCR circuit with $L = 1$ H, $R = 300\ \Omega$ and $C = 20\ \mu	ext{F}$. The rms potential difference across the capacitor is ___ V.

Accepted Answer

50

Question 59

In the experiment to determine the galvanometer resistance by the half-deflection method, the plot of $\dfrac{1}{	heta}$ versus the resistance R of the resistance box is shown in the figure. The figure of merit of the galvanometer is ___ $	imes10^{-1}$ A/division. [The source has emf 2 V.]

Accepted Answer

5

Question 60

Three capacitors of capacitances $25\ \mu	ext{F}$, $30\ \mu	ext{F}$ and $45\ \mu	ext{F}$ are connected in parallel to a supply of 100 V. The energy stored in this combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\dfrac{9}{x}E$. The value of $x$ is ___.

Accepted Answer

86

Question 61

The incorrect postulates of Dalton's atomic theory are: (A) Atoms of different elements differ in mass. (B) Matter consists of divisible atoms. (C) Compounds are formed when atoms of different elements combine in a fixed ratio. (D) All the atoms of a given element have different properties including mass. (E) Chemical reactions involve reorganisation of atoms. Choose the correct answer from the options given below:

Accepted Answer

(D) (B), (D) only

Answer

(A) (B), (D), (E) only

Answer

(B) (A), (B), (D) only

Answer

(C) (C), (D), (E) only

Question 62

The following reaction occurs in the blast furnace where iron ore is reduced to iron metal: $	ext{Fe}_2	ext{O}_3(s) + 3	ext{CO}(g) ightarrow 2	ext{Fe}(l) + 3	ext{CO}_2(g)$. Using Le Chatelier’s principle, predict which one of the following will not disturb the equilibrium.

Accepted Answer

(A) Addition of $	ext{Fe}_2	ext{O}_3$

Answer

(B) Addition of $	ext{CO}_2$

Answer

(C) Removal of CO

Answer

(D) Removal of $	ext{CO}_2$

Question 63

Identify compound (Z) in the following reaction sequence (shown in the figure).

Accepted Answer

(C) (C), (D), (E) only

Answer

(A) (B), (D), (E) only

Answer

(B) (A), (B), (D) only

Answer

(D) All the atoms of given element have different

Question 64

Given below are two statements:
Assertion (A): Enthalpy of neutralisation of a strong monobasic acid with a strong monoacidic base is always $-57$ kJ mol$^{-1}$.
Reason (R): Enthalpy of neutralisation is the amount of heat liberated when one mole of $	ext{H}^+$ ions furnished by the acid combine with one mole of $	ext{OH}^-$ ions furnished by the base to form one mole of water.
In the light of the above statements, choose the correct answer from the options given below.

Accepted Answer

(B) Both (A) and (R) are true and (R) is the correct explanation of (A)

Answer

(A) (A) is true but (R) is false

Answer

(C) (A) is false but (R) is true

Answer

(D) Both (A) and (R) are true but (R) is not the correct explanation of (A)

List-I	List-II
A.Kinetic energy of planet	I. $\dfrac{GMm}{a}$
B.Gravitational potential energy of Sun–planet system	II. $\dfrac{GMm}{2a}$
C.Total mechanical energy of planet	III. $-\dfrac{GMm}{a}$
D.Escape energy at the surface of planet for a unit-mass object	IV. $\dfrac{Gm}{r}$

JEE Main 5 April 2024 Shift 1 Question Paper with Answers

Physics — JEE Main 5 April 2024 Shift 1

Chemistry — JEE Main 5 April 2024 Shift 1

Mathematics — JEE Main 5 April 2024 Shift 1

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